Area and Circumference of Circles
The area and circumference of a circle are found from its radius or diameter using the formulae area = pi x r^2 and circumference = pi x d (or 2 x pi x r). These formulae are essential throughout GCSE geometry, including compound shape, surface area and volume questions.
Before you start
Make sure you're comfortable with these topics first:
Method
- Identify whether you are given the radius or the diameter, and find the other one if needed (radius = diameter / 2).
- For circumference, use C = pi x d or C = 2 x pi x r.
- For area, use A = pi x r^2, making sure you square the radius, not the diameter.
- Use the pi button on your calculator for full accuracy, or the value given in the question, such as pi = 3.14.
- Round your final answer to the accuracy asked for, and always include the correct units, such as cm or cm^2.
Worked example
A circle has radius 9 cm. Work out its area and circumference, both correct to 1 decimal place.
- Circumference: C = 2 x pi x 9 = 56.548...
- Round: C = 56.5 cm (1 d.p.)
- Area: A = pi x 9^2 = pi x 81 = 254.469...
- Round: A = 254.5 cm^2 (1 d.p.)
- Final answer: circumference = 56.5 cm, area = 254.5 cm^2.
Practice questions
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Exam-style questions
Written in the style of a GCSE Maths exam paper, with a full mark scheme.
A circle has radius 6 cm. Work out the circumference of the circle. Give your answer correct to 1 decimal place.
A circular pond has diameter 5.6 m. Work out the area of the pond, correct to 1 decimal place.
A shape is made from a rectangle 10 cm by 6 cm, with a semicircle of diameter 6 cm attached to one of the 6 cm ends. Work out the area of the shape, correct to 1 decimal place.
Free printable worksheet
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